In another question, jasonh mentions a scheme for locking a laser to a resonant cavity called 'tilt locking':

The signal is used for locking the frequency of a laser to a high finesse cavity. The lock has to be stable enough for intensity and phase fluctuations resulting from e.g. acoustic vibrations of the cavity to be strongly suppressed. The error signal is created via the tilt locking scheme, i.e. it is the difference of intensities on two halves of a split photo diode.

I'm familiar with Pound-Drever-Hall locking of a laser cavity, but I've never heard of 'tilt locking' before. How does it work?


1 Answer 1


Consider an optical cavity whose length you want to stabilize such that the cavity stays on resonance with the TEM00 mode of a laser. The basic idea of the tilt locking scheme is to use the phase of an off-resonant mode (TEM10) as a stable phase reference to which the changes in phase of the resonant part (TEM00) of the beam can be compared.

To expand a bit: Also very close to the cavity resonance some part of the TEM00 light is going to be reflected. The phase of this near-resonant light depends extremely sensitively on the exact cavity length (note that here and in what follows I always talk about the phase of the light reflected from the cavity). The phase actually changes sign on resonance so in principle the phase of the reflected TEM00 component could be used as an error signal which--if stabilized to zero using a feedback loop--would keep the cavity on resonance with the TEM00 of the laser.

Unfortunately, you can only measure the phase of the near-resonant mode by comparing it to a stable phase reference in an interferometric measurement. In the tilt locking scheme the TEM10 mode provides you with this phase reference. In most cavities, the TEM10 and TEM00 modes are not resonant simultaneously because of the difference in Gouy phase. Hence, if TEM00 is resonant, TEM10 is off-resonant which means that its phase is very insensitive to the exact cavity length.

To perform the required interferometric measurement you need a split photo diode which is simply a photo diode with two halves, left and right. A split photo diode can detect the intensity of the incoming light on both halves separately plus a circuit which yields the intensity on the left half minus the intensity on the right half. The rest is most easily understood by looking at the picture on page 4 of these nice slides on tilt locking: www.ligo.caltech.edu/docs/G/G000276-00.pdf.

If the beam which is reflected from the cavity is focused onto such a split photo diode the situation is as follows: TEM10 has a positive phase on, say, the left and a negative phase on the right half of the split photo diode. TEM00 on the other hand is completely symmetric and has approximately the same phase in the whole detection area. If TEM00 is exactly on resonance, its phase is zero so that the combined contributions of TEM00 and TEM10 yield the same intensities on both halves, hence the difference is zero.

If TEM00 goes off resonant its phase is not zero anymore. Assume it's positive. Then the light fields of TEM00 and TEM10 are going to interfere constructively on the left half (where also TEM10 has a positive phase) and destructively on the right half (where TEM10 is negative) so that the difference in intensities is positive and the split photo diode produces a positive output voltage.

If on the other hand, the cavity length (or laser frequency) fluctuates in the other direction, TEM00 will acquire a negative phase which means that constructive interference with TEM10 now happens on the right half of the detector and destructive interference on the left half. In this case the split photo diode will produce a negative output voltage.

Hence, the output voltage of the split photo diode can be used as an error signal. From here on everything works the same way as in a Pound-Drever-Hall lock. Advantage: no need for modulation of the laser beam; you only need to make sure that you're not aligning the beam too perfectly to the cavity so that some TEM10 component is present in the reflected beam. Problems may arise due to the high sensitivity of the error signal on the exact location of the beam on the split photo diode; hence, the photo diode should be fixed well and you should not introduce optical components before the split photo diode which may cause significant beam wander.


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